The mean of a data set is the sum of all data elements divided by its count.
The mean weight of the 19 girls is 33.4 kg
Let
[tex]b \to[/tex] boys
[tex]g \to[/tex] girls
[tex]n \to[/tex] the total population
So:
[tex]b = 11[/tex]
[tex]\bar x_b = 31.9[/tex]
[tex]g = 19[/tex]
[tex]n = 30[/tex]
[tex]\bar x = 32.85[/tex]
The mean of all students is calculated as follows:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{\bar x_b \times b + \bar x_g \times g}{n}[/tex]
Substitute known values
[tex]32.85 = \frac{31.9 \times 11 + \bar x_g \times 19}{30}[/tex]
[tex]32.85 = \frac{350.9 + \bar x_g \times 19}{30}[/tex]
Multiply through by 30
[tex]30 \times 32.85 = 350.9 + \bar x_g \times 19[/tex]
[tex]985.5 = 350.9 + \bar x_g \times 19[/tex]
Collect like terms
[tex]985.5 -350.9 = \bar x_g \times 19[/tex]
[tex]634.6 = \bar x_g \times 19[/tex]
Divide through by 19
[tex]33.4 = \bar x_g[/tex]
[tex]\bar x_g = 33.4[/tex]
Hence, the mean weight of the girls is 33.4 kg
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